ln(9x-17)=ln(x+20)

Solution for ln(9x-17)=ln(x+20) equation:

Simplifying
ln(9x + -17) = ln(x + 20)

Reorder the terms:
ln(-17 + 9x) = ln(x + 20)
(-17 * ln + 9x * ln) = ln(x + 20)
(-17ln + 9lnx) = ln(x + 20)

Reorder the terms:
-17ln + 9lnx = ln(20 + x)
-17ln + 9lnx = (20 * ln + x * ln)
-17ln + 9lnx = (20ln + lnx)

Solving
-17ln + 9lnx = 20ln + lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-20ln' to each side of the equation.
-17ln + -20ln + 9lnx = 20ln + -20ln + lnx

Combine like terms: -17ln + -20ln = -37ln
-37ln + 9lnx = 20ln + -20ln + lnx

Combine like terms: 20ln + -20ln = 0
-37ln + 9lnx = 0 + lnx
-37ln + 9lnx = lnx

Add '-1lnx' to each side of the equation.
-37ln + 9lnx + -1lnx = lnx + -1lnx

Combine like terms: 9lnx + -1lnx = 8lnx
-37ln + 8lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-37ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-37 + 8x) = 0

Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

Move all terms containing l to the left, all other terms to the right.

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-37 + 8x)' equal to zero and attempt to solve:

Simplifying
-37 + 8x = 0

Solving
-37 + 8x = 0

Move all terms containing l to the left, all other terms to the right.

Add '37' to each side of the equation.
-37 + 37 + 8x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 8x = 0 + 37
8x = 0 + 37

Combine like terms: 0 + 37 = 37
8x = 37

Add '-8x' to each side of the equation.
8x + -8x = 37 + -8x

Combine like terms: 8x + -8x = 0
0 = 37 + -8x

Simplifying
0 = 37 + -8x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.